Quadratic Roots & Solving Quadratics by Factoring

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero. They can be found using factoring, completing the square, or the quadratic formula.

Front

How do you factor a quadratic equation?

Back

To factor a quadratic equation, express it in the form (px + q)(rx + s) = 0, where p, q, r, and s are constants that satisfy the equation.

Front

What is the zero-product property?

Back

The zero-product property states that if the product of two factors is zero, then at least one of the factors must be zero.

Front

How do you find the roots of the equation 12x = 9x² + 4?

Back

Rearrange to 9x² - 12x + 4 = 0, then factor to (3x - 2)(3x - 2) = 0, giving roots x = 2/3.

Front

What are the solutions to the equation 7(x-10)(3x+2) = 0?

Back

Set each factor to zero: x - 10 = 0 (x = 10) and 3x + 2 = 0 (x = -2/3). Solutions are x = 10 and x = -2/3.

Front

What does it mean for a function to have zeros?

Back

Zeros of a function are the x-values where the function's output is zero, indicating the points where the graph intersects the x-axis.

Front

How do you determine the zeros from a graph?

Back

Identify the x-coordinates of the points where the graph intersects the x-axis.

Front

What is an ordered pair in the context of quadratic roots?

Back

An ordered pair (x, 0) represents the x-coordinate of the root of the quadratic equation, indicating where the graph crosses the x-axis.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, representing the maximum or minimum value of the function.